TTField treatment with optimization of electrode positions on the head based on MRI-based conductivity measurements

ABSTRACT

When electrodes are used to impose an electric field in target tissue within an anatomic volume (e.g., to apply TTFields to treat a tumor), the position of the electrodes can be optimized by obtaining electrical conductivity measurements in an anatomic volume and generating a 3D map of the conductivity directly from the obtained electrical conductivity or resistivity measurements, without segmenting the anatomic volume into tissue types. A location of the target tissue is identified within the anatomic volume, and the positions for the electrodes are determined based on the 3D map of electrical conductivity and the position of the target tissue.

CROSS REFERENCE TO RELATED APPLICATIONS

This Application is a divisional of U.S. patent application Ser. No.15/336,660 filed Oct. 27, 2016, which claims the benefit of U.S.Provisional Applications 62/247,314 filed Oct. 28, 2015, and 62/294,372filed Feb. 12, 2016, all of which are incorporated herein by referencein their entirety.

BACKGROUND

Tumor Treating Fields, or TTFields, are low intensity (e.g., 1-3 V/cm)alternating electric fields within the intermediate frequency range(100-300 kHz). This non-invasive treatment targets solid tumors and isdescribed in U.S. Pat. No. 7,565,205, which is incorporated herein byreference in its entirety. TTFields disrupt cell division throughphysical interactions with key molecules during mitosis. TTFieldstherapy is an approved mono-treatment for recurrent glioblastoma, and anapproved combination therapy with chemotherapy for newly diagnosedpatients. These electric fields are induced non-invasively by transducerarrays (i.e., arrays of electrodes) placed directly on the patient'sscalp. TTFields also appear to be beneficial for treating tumors inother parts of the body.

TTFields are established as an anti-mitotic cancer treatment modalitybecause they interfere with proper micro-tubule assembly duringmetaphase and eventually destroy the cells during telophase andcytokinesis. The efficacy increases with increasing field strength andthe optimal frequency is cancer cell line dependent with 200 kHz beingthe frequency for which inhibition of glioma cells growth caused byTTFields is highest. For cancer treatment, non-invasive devices weredeveloped with capacitively coupled transducers that are placed directlyat the skin region close to the tumor. For patients with GlioblastomaMultiforme (GBM), the most common primary, malignant brain tumor inhumans, the device for delivering TTFields therapy is called Optune™.

Because the effect of TTFields is directional with cells dividingparallel to the field affected more than cells dividing in otherdirections, and because cells divide in all directions, TTFields aretypically delivered through two pairs of transducer arrays that generateperpendicular fields within the treated tumor. More specifically, forthe Optune system one pair of electrodes is located to the left andright (LR) of the tumor, and the other pair of electrodes is locatedanterior and posterior (AP) to the tumor. Cycling the field betweenthese two directions (i.e., LR and AP) ensures that a maximal range ofcell orientations is targeted.

In-vivo and in-vitro studies show that the efficacy of TTFields therapyincreases as the intensity of the electric field increases. Therefore,optimizing array placement on the patient's scalp to increase theintensity in the diseased region of the brain is standard practice forthe Optune system. To date, array placement optimization is done eitherby rule of thumb (e.g., placing the arrays on the scalp as close to thetumor as possible) or using the NovoTal™ syste NovoTal™ uses a limitedset of measurements describing the geometry of the patient's head, thetumor dimensions and its location to find an optimal array layout. Themeasurements used as input for NovoTal™ are manually derived from thepatient MRIs by the physician. The NovoTal™ optimization algorithmrelies on a generic understanding of how the electric field distributeswithin the head as a function of the positions of the array, and doesnot take account for variations in the electrical property distributionswithin the heads of different patients. These variations may influencethe field distribution within the head and tumor, leading to situationsin which e layouts that NovoTal™ recommends are sub-optimal.

SUMMARY OF THE INVENTION

One aspect of the invention is directed to a first method of optimizingpositions of a plurality of electrodes placed on a subject's body,wherein the electrodes are used to impose an electric field in targettissue within an anatomic volume. The first method comprising the stepsof obtaining electrical conductivity or resistivity measurements in theanatomic volume, and generating a 3D map of electrical conductivity orresistivity of the anatomic volume directly from the obtained electricalconductivity or resistivity measurements, without segmenting theanatomic volume into tissue types. This method also includes the stepsof identifying a location of the target tissue within the anatomicvolume, and determining positions for the electrodes based on the 3D mapof electrical conductivity or resistivity generated in the generatingstep and the location of the target tissue identified in the identifyingstep.

Some embodiments of the first method further comprise the steps ofaffixing the electrodes to the subject's body at the positionsdetermined in the determining step, and applying electrical signalsbetween the electrodes subsequent to the affixing step, so as to imposethe electric field in the target tissue.

In some embodiments of the first method, the measurements obtained inthe obtaining step represent the diffusion of molecules. In someembodiments of the first method, the obtaining step comprises acquiringMRI data using diffusion weighted imaging. In some embodiments of thefirst method, the obtaining step comprises acquiring MRI data usingcustomized multi echo gradient sequences.

In some embodiments of the first method, the obtaining step comprisesacquiring MRI data using diffusion tensor imaging. Optionally, in theseembodiments, the step of acquiring MRI data using diffusion tensorimaging comprises a direct mapping method that assumes a linearrelationship between eigenvalues of diffusion and conductivity tensors,σv=s·dv, where σv and dv are the with eigenvalues of the conductivityand the diffusion respectively. Optionally, in these embodiments, thestep of acquiring MRI data using diffusion tensor imaging comprises avolume normalized method in which a geometric mean of conductivitytensors eigenvalues in each volume element in the anatomic volume arematched locally to specific isotropic conductivity values of a tissuetype to which the volume element belongs.

In some embodiments of the first method, the anatomic volume compriseswhite matter and grey matter of a brain.

In some embodiments of the first method, the anatomic volume is a brain,and the determination of positions for the electrodes is based on acomposite model in which the 3D map of electrical conductivity orresistivity of the brain is surrounded by a model of a first shellhaving a first constant conductivity. In these embodiments, the model ofthe first shell may represent a scalp, a skull, and CSF, taken together.Alternatively, in these embodiments, the model of the first shell mayrepresent CSF, the composite model further includes a second shell thatrepresents a skull, the second shell having a second constantconductivity, and the composite model further includes a third shellthat represents a scalp, the third shell having a third constantconductivity. In these embodiments, the step of determining positionsfor the electrodes may comprise adding a dipole to the composite modelat a location that corresponds to the target tissue and selectingexternal positions at which a potential attributable to the dipole ismaximum.

In some embodiments of the first method, the step of determiningpositions for the electrodes comprises calculating positions for theelectrodes that will provide a maximum intensity of the electric fieldin the target tissue. In some embodiments of the first method, in thegenerating step, the 3D map has a resolution that is higher than 1 mm×1mm×1 mm. In some embodiments of the first method, the step of generatinga 3D map comprises generating a simple geometric object representing theanatomic volume.

In some embodiments of the first method, the step of generating a 3D mapcomprises classifying a tissue type for each volume element based on afractional anisotropy. In some embodiments of the first method, the stepof generating a 3D map comprises classifying a tissue type for eachvolume element based on a mean conductivity. In some embodiments of thefirst method, the step of generating a 3D map comprises matchinggeometric means of conductivity tensors' eigenvalues to specificisotropic reference values.

Another aspect of the invention is directed to a second method ofcreating a model of a mammal's head. The head includes brain tissue,CSF, a skull, and a scalp. This method comprises the steps of modeling aregion of the head that corresponds to brain tissue using a 3D set ofconductivity tensors, and modeling the CSF, the skull, and the scalpusing at least one shell having a constant conductivity.

In some embodiments of the second method, the step of modeling theregion of the head that corresponds to brain tissue using a 3D set ofconductivity tensors is implemented without identifying boundariesbetween different types of a healthy brain tissue.

In some embodiments of the second method, the 3D set of conductivitytensors is obtained using MRI. In some of these embodiments, the 3D setof conductivity tensors is derived from a diffusion tensor imagingdataset.

In some embodiments of the second method, the step of modeling the CSF,the skull, and the scalp comprises the steps of modeling the CSF as afirst shell disposed outside the brain tissue and in contact with thebrain tissue, the first shell having a first constant conductivity;modeling the skull as a second shell disposed outside the CSF and incontact with the CSF, the second shell having a second constantconductivity; and modeling the scalp as a third shell disposed outsidethe skull and in contact with the skull, the third shell having a thirdconstant conductivity.

In some embodiments of the second method, the step of modeling the CSF,the skull, and the scalp comprises the step of modeling the CSF, theskull, and the scalp, taken together, as a single shell disposed outsidethe brain tissue and in contact with the brain tissue, the single shellhaving a constant conductivity.

Some embodiments of the second method further comprise the steps ofidentifying a location of a target tissue within the brain tissue, anddetermining positions for a plurality of electrodes based on thelocation of the target tissue identified in the identifying step, the 3Dset of conductivity tensors, and the conductivity of the at least oneshell. Optionally, these embodiments further comprise the steps ofaffixing the electrodes to the mammal's head at the positions determinedin the determining step, applying electrical signals between theelectrodes subsequent to the affixing step, so as to impose an electricfield in the target tissue. Optionally, in these embodiments, the stepof determining positions for the electrodes comprises modeling a dipoleat a location that corresponds to the target tissue and selectingpositions at which a potential attributable to the dipole is maximum.Optionally, in these embodiments, the step of determining positions forthe electrodes comprises calculating positions for the electrodes thatwill provide optimal combined treatment specifications in the targettissue.

In some embodiments of the second method, the step of modeling a regionusing a 3D set of conductivity tensors comprises classifying a tissuetype for each volume element based on a fractional anisotropy. In someembodiments of the second method, the step of modeling a region using a3D set of conductivity tensors comprises classifying a tissue type foreach volume element based on a mean conductivity. In some embodiments ofthe second method, the step of modeling a region using a 3D set ofconductivity tensors comprises matching geometric means of conductivitytensors' eigenvalues to specific isotropic reference values.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of one example for creating a model of a head andoptimizing the electric field using that model.

FIG. 2 depicts electric field distributions in various cross-sectionsthrough a virtual tumor in three different models created using the sameMRI data set.

FIG. 3 depicts the electric field distribution for three anisotropicmodels in one axial slice through the tumor.

FIG. 4 depicts a front view of the scalp with transducer arrays affixedto the scalp.

FIGS. 5A and 5B respectively depict a set of shells for two differentmodels.

FIGS. 6A and 6B depict side and the top views, respectively, ofventricles and a virtual tumor inside a white matter shell.

FIG. 7 depicts the conductivity map and resulting electric fielddistributions in the cortical and tumor tissues in an axial slice forfive respective models.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

One approach to overcoming the limitations of the NovoTal™ system is tooptimize array layouts based on accurate calculations of the electricfield distributions within the patients head as a function of arrayposition. The patient can be a human or other type of mammal or otheranimals. This can be done by constructing realistic computational modelsdescribing the distribution of conductivity within the patient's head.This can be achieved using MRI data. However, to date, deriving suchrealistic computational head models is time consuming and requires a lotof manual intervention. The reason for this is that the models areobtained by segmenting the MR images into various tissue types andassigning representative conductivity values to each tissue type.Although the segmentation of the outer layers of the head, like thescalp, skull and cerebrospinal fluid (CSF) might be achieved withstandard software without major difficulties, the cortical tissues havevery complex geometric patterns and are much more complicated toprocess.

Although automatic and semi-automatic algorithms for segmenting thecortical tissues do exist, their performance is generally not sufficientfor creating detailed models. Furthermore, the performance of corticaltissue segmentation algorithms deteriorates further when patient MRIswith large distortions due to tumor tissue and edema are present in thebrain, and therefore extensive user intervention is required for thistask. Hence, creating realistic computational head models of patientsthrough rigorous segmentation of MR images is extremely labor-intensiveand time consuming.

This application describes a work-flow for creating realistic headmodels for simulating TTFields with minimal user intervention, as wellas details on how these head models can be used to optimize TTFieldsarray layouts on patients. In the approach presented here, conductivityvalues in the head model are determined directly from MRI-basedconductivity measurements. Therefore, the need for complex and accuratesegmentation is removed, reducing the time and human labor required tocreate a computational head model of a patient. Once the realistic modelhas been constructed, the optimization can be performed in a fully orsemi-automatic manner using a sequence of algorithms that is alsodescribed herein.

For convenience, this description is divided into three parts: Part 1provides a detailed description of methods for creating realistic headmodels for TTFields simulations from MRI data with minimal userintervention. Part 2 provides a detailed description on how to optimizeTTFields array positions using the model created in part 1. And part 3describes proof of concept for the creation of realistic head models forTTTields simulations with minimal user intervention, using simple convexhulls to model the outer layers and a conductivity map to model thebrain.

FIG. 1 is a flowchart of one example for creating the model (in stepsS11-S14) and optimizing the electric field using that model (stepsS21-S24).

Part 1: Creation of a realistic computational phantom from MRI data.

Creating an accurate computational phantom preferably involvesaccurately mapping the electric properties (e.g., conductivity,resistivity) at each point within the computational phantom. Onetraditional method for creating computational phantoms involvessegmentation of the head into different tissue types with distinctisotropic electric properties. When building a model using this method,it is important to accurately identify the boundaries of each tissuetype in 3D space so that the electric properties for each tissue typeare mapped accurately into the model.

The embodiments described herein overcome the need for rigoroussegmentation by using MRI sequences such as Diffusion Weighted Imaging(DWI), Diffusion Tensor Imaging (DTI), or customized multi echo gradientsequences (GRE) to directly estimate the electric properties at eachpoint in 3D space. Mapping the electric properties directly using MRIsequences reduces the need for accurate tissue segmentation because theelectric properties of every point are defined directly from the MRI,and not from the tissue type to which they are assigned to during thesegmentation. Therefore, the segmentation process can be simplified oreven eliminated without compromising the accuracy of the computationalphantom. Note that while the embodiments described herein discussmapping conductivity, alternative embodiments can provide similarresults by mapping a different electrical property such as resistivity.

Steps S11-S14 in FIG. 1 depict one example of a set of steps that may beused to generate a computational phantom representing a patient based onMRI conductivity measurements.

Step S11 is the image acquisition step. In this step, both structuraldata and data from which conductivity maps can be calculated areacquired. Structural data can be obtained for instance from standard T₁and T₂ MRI sequences. Conductivity can be obtained using a variety ofMRI data acquisition modes such as DWI, DTI or GRE. In order to create agood computational phantom, high resolution images should be obtained. Aresolution of at least 1 mm×1 mm×1 mm for both structural andconductivity-related images is preferable. Lower resolution images maybe used for one or both of these types of images, but the lowerresolution will yield less accurate phantoms.

The data set is preferably inspected and images affected by largeartifacts are preferably removed. Preferably some scanner-specificpre-processing is applied. For example, images may be converted fromDICOM format to NIFTI. A different step of preprocessing may be toregister all images to a standard space (for example the MontrealNeurological Institute, MNI, space). This can be done using readilyavailable software packages including but not limited to FSI, FLIRT, andSPM.

Step S12 is the step of processing structural images. As mentionedabove, the work-flow presented here utilizes MRI-based conductivitymeasurements to create the computational phantom. However, structuralimages may still be used to identify the boundaries of the head, as wellas identify regions belonging to specific tissues within the brain inwhich it might be advantageous to assign typical conductivity valuesthat are not derived from the MRI measurements. For instance, in somecases it may be advantageous to identify (and segment) the skull, scalpand CSF within the images, and assign typical conductivity values to theregions corresponding to these tissues (but still rely on the capitalMRI-based measurements for the regions corresponding to the brain).

It is possible to use available software packages to obtain a detailedsegmentation of these three tissue types, as well as the ventricles.However, due to the complexity of some of these structures, this stillmay require significant manual intervention. Therefore, simplifiedschemes for building the head model may be beneficial. One possibilityto downgrade the complexity of creating the phantom is to simplify thegeometry representing the outer model layers (scalp, skull and CSF). Forexample, shells or convex hulls of the outer tissues could be used as amodel of those layers. If a rough segmentation of the outer layers isavailable, the creation of the corresponding convex hull is trivial andcan be performed using standard algorithms and software. Another optionis for the user to measure the thickness of the three outer layers(scalp, skull and CSF) at a representative region (a region where thetransducer arrays might be placed) through examination of the structuralimage. These measurements can be used to create three concentric shellsor layers which represent the scalp, skull, and the CSF. These layersmight be obtained by deforming a default oval structure, which could bea default convex hull of a scalp segmentation.

Steps S13 and S14 both deal with processing of DTI images. Step S13 isthe step of preprocessing of images and tensor estimation. DTImeasurements involve acquisition of multiple images acquired withdifferent imaging conditions. Each image is characterized by itsgradient direction and b-value. For processing DTI images, the gradientdirections and b-values first need to be extracted. This can beperformed using standard software. Once the gradient directions andb-values have been extracted, the images are preferably corrected fordistortions which arise from sample motion (e.g., head movements) aswell as from distortion to the MRIs that arise from eddy currentsgenerated during data acquisition. In addition, the images arepreferably registered to overlap with the structural images discussed inthe previous stage. Correction of distortions and registration can beperformed using standard software packages. After this preprocessing hasbeen completed, the diffusion tensors at each point in relevant regionsof the model can be estimated.

Many software bundles for deriving the diffusion tensors from DTI imagesexist. For example, A Hitchhiker's Guide to Diffusion Tensor Imaging byJ. M. Soares et al., frontiers in Neuroscience, vol. 7, article 31, p.1-14, doi: 10.3389/fnins.2013.00031, 2013 includes a detailed summary ofavailable software for the estimation of the tensors and also forpreprocessing of DTI. Two options for deriving the diffusion tensorsfrom all images were tested. The first option uses the ESL diffusiontoolbox for correction and registration of the images and calculatingthe principal directions (eigenvectors), principal diffusivities(eigenvalues), and the fractional anisotropy. The second option was touse the DIFFPREP module from the Tortoise software in order to performthe motion and eddy current distortion correction with a B-matrixreorientation. Then the DIFFCALC module can be used for the estimationof the diffusion tensor in each voxel and for the computation oftensor-derived quantities. In both software packages it is possible toreorient the data set with B-matrix reorientation to a standard frame ofreference, which naturally is the structural image.

Step S14 is the step of mapping conductivity within the computationalphantom. In this step, conductivity values are mapped to each volumeelement within the computational phantom. In regions belonging to tissuetypes where the segmentation is sufficiently accurate (e.g., the skullor CSF), representative isotropic conductivity values for each tissuetype may be assigned. In other regions, conductivity values are assignedbased on the MRI-based conductivity measurements, such as DTI.

Deriving conductivity values from DTI data follows the proposition thatthe conductivity tensors share the same eigenvectors as the effectivediffusion tensor. Once the diffusion tensor has been estimated for eachvolume element that was imaged, an estimate of the conductivity tensorscan be formed using any suitable approach, some of which are describedin detail in How the Brain Tissue Shapes the Electric Field induced byTranscranial Magnetic Stimulation by A. Opitz et al. Neuroimage, vol.58, no, 3, pp. 849-59, October 2011. For example, one suitable method iscalled direct mapping (dM), which assumes a linear relationship betweenthe eigenvalues of the diffusion and conductivity tensors, i.e.,σ_(v)=s·d_(v), where σ_(v) and d_(v) are the v-th eigenvalues of theconductivity and the diffusion respectively, Different assumptions onthe scaling factor can be used, whereas also an adapted scaling factorscan be applied following. See e.g., EEG Source Analysis of EpileptiformActivity Using a 1 mm Anisotropic Hexahedra Finite Element Head Model byM. Rullmann et al. NeuroImage 44, 399-410 (2009). Another suitablemethod is the volume normalized (vN) method in which the geometric meanof the conductivity tensor's eigenvalues in each volume element in thebrain are matched locally to the specific isotropic conductivity valuesof the tissue type to which the element belongs. See e.g., Influence ofAnisotropic Electrical Conductivity in White Matter Tissue on theEEG/MFG Forward and Inverse Solution—A High-Resolution Whole HeadSimulation Study, by D. Güllmar NeuroImage 51, 145-163 (2010).

Both of these methods could be used to map conductivity to the relevantregions (mainly cortical region) within the computational phantom.However, the vN method requires a higher degree of accuracy in thesegmentation, as conductivity values are mapped at each volume elementusing information about the tissue type in that area. Therefore,assigning a volume element to the wrong tissue type would result in anerror in the conductivity map within the computational phantom. On theother hand, for the dM method the conductivity values are assigned toall elements using the same linear relationship regardless of the tissuetype at the area. Therefore, dM of DTI data may be more useful than thevN mapping of DTI data for simplifying the pipeline for creatingcomputational phantoms for TTFields simulations. Note, however, that theconstant scaling factor in dM may only lead to accurate values in thehealthy tissues, and may be less than optimal for the tumor tissues.

Alternative mapping methods could also be applied. For example, in orderto overcome the limitation of the vN method (a segmentation needs to bepresent to be able to assign each volume element to a specific tissuetype), the tissue type of the volume element could also be classified byits fractional anisotropy, mean conductivity, or other related measures.Alternatively, the geometric mean of the conductivity tensor'seigenvalues could be matched to a specific isotropic reference value.This would be a general way to segment or classify tissue ypes (possiblyeven creating a full model) only from DTI data. Note that when thefractional anisotropy (or any other measure that can be derived from theconductivity data) is found, then the neighboring elements arepreferably checked to avoid outliers (for example, to eliminate a GMpoint that was identified inside the WM).

Part 2: Optimization of TTFields Array Positions Using Realistic HeadModels

Optimization of array layouts means finding the array layout thatoptimizes the electric field within the diseased regions of thepatient's brain (tumor). This optimization may be implemented byperforming the following four steps: (S21) identifying the volumetargeted for treatment (target volume) within the realistic head model;(S22) automatically placing transducer arrays and setting boundaryconditions on the realistic head model; (S23) calculating the electricfield that develops within the realistic head model once arrays havebeen placed on the realistic head model and boundary conditions applied;and (S24) running an optimization algorithm to find the layout thatyields optimal electric field distributions within the target volume. Adetailed example for implementing these four steps is provided below.

Step S21 involves locating the target volume within the realistic headmodel (i.e., defining a region of interest). A first step in finding alayout that yields optimal electric field distributions within thepatient's body is to correctly identify the location and target volume,in which the electric field should be optimized.

In some embodiments, the target volume will be either the Gross TumorVolume (GTV) or the Clinical Target Volume (CTV). The GTV is the grossdemonstrable extent and location of the tumor, whereas the CTV includesthe demonstrated tumors if present and any other tissue with presumedtumor. In many cases the CIV is found by defining a volume thatencompasses the GTV and adding a margin with a predefined width aroundthe GTV.

In order to identify the GTV or the CTV, it is necessary to identify thevolume of the tumor within the MRI images. This can be performed eithermanually by the user, automatically, or using a semi-automatic approachin which user-assisted algorithms are used. When performing this taskmanually, the MRI data could be presented to a user, and the user couldbe asked to outline the volume of the CTV on the data. The datapresented to the user could be structural MRI data (e.g., T₁, T₂ data).The different MRI modalities could be registered onto each other, andthe user could be presented with the option to view any of the datasets,and outline the CTV. The user could be asked to outline the CTV on a 3Dvolumetric representation of the MRIs, or the user could be given theoption of viewing individual 2D slices of the data, and marking the CTVboundary on each slice. Once the boundaries have been marked on eachslice, the CTV within the anatomic volume (and hence within therealistic model) can be found. In this case, the volume marked by theuser would correspond to the GTV. In some embodiments, the CTV couldthen be found by adding margins of a predefined width to the GTV.Similarly, in other embodiments, the user might be asked to mark the CTVusing a similar procedure.

An alternative to the manual approach is to use automatic segmentationalgorithms to find the CTV. These algorithms perform automaticsegmentation algorithms to identify the UV using either the structuralMRI data, or possibly the DTI data. Note that DTI data can be used forsegmentation for this purpose because the diffusion tensor within thetumor (and any edema region) will be different from its surroundings.

However, as mentioned above, current fully automatic segmentationalgorithms may not be sufficiently stable. Therefore, semi-automaticsegmentation approaches of the MRI data may be preferable. In an exampleof these approaches, a user iteratively provides input into thealgorithm (e.g., the location of the tumor on the images, roughlymarking the boundaries of the tumor, demarcating a region of interest inwhich the tumor is located), which is then used by a segmentationalgorithm. The user may then be given the option to refine thesegmentation to gain a better estimation of the CTV location and volumewithin the head.

Whether using automatic or semi-automatic approaches, the identifiedtumor volume would correspond with the GTV, and the CTV could then befound automatically by expanding the GTV volume by a pre-defined amountdefining the CTV as a volume that encompasses a 20 mm wide margin aroundthe tumor).

Note that in some cases, it might be sufficient for the user to define aregion of interest in which they want to optimize the electric field.This region of interest might be for instance a box volume, a sphericalvolume, or volume of arbitrary shape in the anatomic volume thatencompasses the tumor. When this approach is used, complex algorithmsfor accurately identifying the tumor may not be needed.

Step S22 involves automatically calculating the position and orientationof the arrays on the realistic head model for a given iteration. Eachtransducer array used for the delivery of TTFields in the Optune™ devicecomprise a set of ceramic disk electrodes, which are coupled to thepatient's head through a layer of medical gel. When placing arrays onreal patients, the disks naturally align parallel to the skin, and goodelectrical contact between the arrays and the skin occurs because themedical gel deforms to match the body's contours. However, virtualmodels are made of rigidly defined geometries. Therefore, placing thearrays on the model requires an accurate method for finding theorientation and contour of the model surface at the positions where thearrays are to be placed, as well as finding the thickness/geometry ofthe gel that is necessary to ensure good contact of the model arrayswith the realistic patient model. In order to enable fully automatedoptimization of field distributions these calculations have to beperformed automatically.

A variety of algorithms to perform this task may be used. The steps ofone such algorithm recently devised for this purpose are set forthbelow.

-   -   a. Define the position at which the central point of the        transducer array will be placed on the model head. The position        could be defined by a user or as one of the steps in the field        optimization algorithm which are discussed in step S24.    -   b. Using the input from step (a) in conjunction with knowledge        about the geometry of the disks and how the disks are arranged        in the array, calculate the approximate positions of the centers        of all disks in the transducer array within the model.    -   c. Calculate the orientations of the surface of the realistic        model at the positions where the disks are to be placed. The        calculation is performed by finding all points on the        computational phantom skin that are within a distance of one        disk radius from the designated center of the disk. The        coordinates of these points are arranged into the columns of a        matrix, and singular value decomposition performed on the        matrix. The normal to the model skin is then the eigenvector        that corresponds to the smallest eigenvalue found.    -   d. For each disk in the transducer array: calculate the        thickness of the medical gel that is required to ensure good        contact between the disks and the patient's body. This is done        by finding the parameters for a cylinder with its height        oriented parallel to the skin surface normal. The cylinder is        defined with a radius equal to the radius of the disks, and its        height set to extend a pre-determined amount (this is a        pre-determined constant) beyond the points on the skin used to        find the normal. This results in a cylinder that xtends at-least        the pre-determined amount out from the phantom surface.    -   e. On the model, create the cylinders described in (d).    -   f. Through binary logical operations (e.g., subtract head from        cylinder) remove from the model the regions of the cylinder that        protrude into the realistic model of the patient. The resulting        “truncated cylinders” represent the medical gel associated with        the transducer arrays    -   g. On the outer side of the “truncated cylinders” place disks        that represent the ceramic disks of the transducer arrays.

Step S23 involves calculating the electric field distribution within thehead model for the given iteration. Once the head phantom is constructedand the transducer arrays (i.e., the electrode arrays) that will be usedto apply the fields are placed on the realistic head model, then avolume mesh, suitable for finite element (FE) method analysis, can becreated. Next boundary conditions can be applied to the model. Examplesof boundary conditions that might be used include Dirichlet boundary(constant voltage) conditions on the transducer arrays, Neumann boundaryconditions on the transducer arrays (constant current), or floatingpotential boundary condition that set the potential at that boundary sothat the integral of the normal component of the current density isequal to a specified amplitude. The model can then be solved with asuitable finite element solver (e.g., a low frequency quasistaticelectromagnetic solver) or alternatively with finite difference (FD)algorithms. The meshing, imposing of boundary conditions and solving ofthe model can be performed with existing software packages such asSim4Life, Comsol Multiphysics, Ansys, or Matlab. Alternatively, customcomputer code that realizes the FE (or FD) algorithms could be written.This code could utilize existing open-source software resources such asC-Gal (for creating meshes), or FREEFEM++ (software written in C++ forrapid testing and finite element simulations). The final solution of themodel will be a dataset that describes the electric field distributionor related quantities such as electric potential within thecomputational phantom for the given iteration.

Step 24 is the optimization step. An optimization algorithm is used tofind the array layout that optimizes the electric field delivery to thediseased regions of the patient's brain (tumor) for both applicationdirections (IR and AP, as mentioned above), The optimization algorithmwill utilize the method for automatic array placement and the method forsolving the electric field within the head model in a well-definedsequence in order to find the optimal array layout. The optimal layoutwill be the layout that maximizes or minimizes some target function ofthe electric field in the diseased regions of the brain, consideringboth directions at which the electric field is applied. This targetfunction may be for instance the maximum intensity within the diseasedregion or the average intensity within the diseased region. It alsopossible to define other target functions.

There are a number of approaches that could be used to find the optimalarray layouts for patients, three of which are described below, Oneoptimization approach is an exhaustive search. In this approach theoptimizer will include a bank with a finite number of array layouts thatshould be tested. The optimizer performs simulations of all arraylayouts in the bank (e.g., by repeating steps S22 and S23 for eachlayout), and picks the array layouts that yield the optimal fieldintensities in the tumor (the optimal layout is the layout in the bankthat yields the highest (or lowest) value for the optimization targetfunction, e.g., the electric field strength delivered to the tumor).

Another optimization approach is an iterative search. This approachcovers the use of algorithm such as minimum-descent optimization methodsand simplex search optimization. Using this approach, the algorithmiteratively tests different array layouts on the head and calculates thetarget function for electric field in the tumor for each layout. Thisapproach therefore also involves repeating steps S22 and S23 for eachlayout. At each iteration, the algorithm automatically picks theconfiguration to test based on the results of the previous iteration.The algorithm is designed to converge so that it maximizes (orminimizes) the defined target function for the field in the tumor.

Yet another optimization approach is based on placing a dipole at thecenter of the tumor in the model. This approach differs from the othertwo approaches, as it does not rely on solving field intensity fordifferent array layouts. Rather, the optimal position for the arrays isfound by placing a dipole aligned with the direction of the expectedfield at the center of the tumor in the model, and solving theelectromagnetic potential. The regions on the scalp where the electricpotential (or possibly electric field) is maximal will be the positionswhere the arrays are placed. The logic of this method is that the dipolewill generate an electric field that is maximal at the tumor center. Byreciprocity, if we were able to generate the field/voltage on the scalpthat the calculation yielded, then we would expect to obtain a fielddistribution that is maximal at the tumor center (where the dipole wasplaced). The closest we can practically get to this with our currentsystem is to place the arrays in the regions where the potential inducedby the dipole on the scalp is maximal.

Note that alternative optimization schemes can be used to find an arraylayout that optimizes the electric field within diseased regions of thebrain. For example, algorithms that combine the various approachesmentioned above. As an example of how these approaches may be combined,consider an algorithm in combining the third approach discussed above(i.e., positioning the dipole at the center of the tumor in the model)with the second approach (i.e., the iterative search). With thiscombination, an array layout is initially found using the dipole at thecenter of the tumor approach. This array layout is used as input to aniterative search that finds the optimal layout.

Part 3: Proof of Concept that Simplified Head Models Can be Constructedand Yield Accurate Results.

Proof of concept was based on modifications to a previously developedrealistic human head model that incorporated anisotropic conductivityvalues of the cortical tissues. This model originated from a healthysubject, so that the tumor had to be represented by a virtual lesion.The phantom has already been used to calculate the electric fielddistribution following TTFields application.

In order to test the concept, first convex hulls of all tissue typeswere created, except the ventricles. The cystic tumor in this model wasrepresented by two concentric spheres, an active shell surrounding thenecrotic core. It was placed in the right hemisphere close to thelateral ventricle.

FIG. 2 shows the electric field distribution in various cross-sectionsthrough the tumor of three different models created using the same MRIdata set. More specifically, FIG. 2 shows the results for bothperpendicular configurations used for TTFields treatment: the left andright (LR) array (panels 21-23), and the array in the anterior andposterior (AP) parts of the head (panels 24-26). Panels 21 and 24 showresults for the classic modelling approach, the realistic head model, inwhich the MRI is accurately segmented and representative isotropicdielectric properties of each tissue are assigned to all volume elementsbelonging to that tissue. Panels 22 and 24 show results for thesimplified modeling approach in which tissue types are segmented asconvex hulls, and representative isotropic dielectric properties areassigned to each tissue type. Panels 23 and 26 show results of thesimplified model in which conductivity values are assigned to eachvolume element of the cortical tissues (GM, WM, and cerebellum) based onconductivity maps derived from DTI images.

The correlation between the various modeling approaches is strong. Morespecifically, the TTFields-induced electric field distribution withinthe brain and tumor of the realistic head model is non-uniform. Thismeans that although the field intensity is highest close to the activetransducer arrays, additional hotspots are induced in the center of thehead (in tissues with the lower conductivity close to boundaries towhich the electric field is perpendicular), as seen in panels 21 and 24.In the isotropic simplified model, as a result of the smooth tissueinterfaces, the field distribution is merely decaying away from thetransducers. Nonetheless because heterogeneous dielectric properties areused, the “usual” hotspots are seen close to the ventricles and alsowithin the tumor's active shell. Closely observing the fielddistribution inside the tumor, reveals very similar patterns in theoriginal and the simple isotropic model, as seen in panels 22 and 25.Incorporating anisotropic conductivity tensors in the brain tissuesresults in even more similar electric field distributions within thebrain, as seen in panels 23 and 26. It appears that the gyri are visibleas well as some major fiber tracts and the current flow through thembecomes notable.

When comparing the average electric field values in the tumor ascalculated using the realistic vs the simplified model, the percentagedifference for the isotropic models is less than 6%. When the realisticanisotropic model is compared to the simplified anisotropic model, thepercentage difference between average field strength in the tumor shellis less than 5%. In both cases the slightly lower values are predictedfor the simplified model.

In FIG. 3 the electric field distribution is again presented in oneaxial slice through the virtual tumor. In each of the panels 31-33, theelectric field distribution in this axial slice for the LR and AP arraysappears at the top and bottom of the panel, respectively. The originalmodel (panel 31) corresponds to the realistic representation of alltissues with dM anisotropy for the cortical tissues. The simple1 model(panel 32) also uses dM anisotropic conductivity tensors for thecortical tissues (represented by convex hulls) and it employs convexhull or shells of all surfaces except the ventricles, all of which haveisotropic conductivity values. The simple2 model (panel 33) is similarto the simple1 model, but a detailed representation of the ventricles isneglected, whereas their presence is accounted for by using anisotropicconductivity tensors derived for this region from the DTI data (for theoriginal and the simple1 model this data was neglected or overwritten bythe ventricle segmentation with an isotropic conductivity value). Table1 compiles the corresponding average field strength values in the brainand the two tumor tissues. Since this virtual lesion is close to theventricles the field in the tumor is more affected by the ongoingsimplification. Still the differences are relatively small, whereas theaverage field in the tumor induced by the LR array is increased to 114%in the original realistic model (compared to the simple2) model andreduced to 95% in the AP stimulation.

TABLE 1 LR AP Brain shell core Brain shell core avg(E) original 1.391.76 0.82 1.43 1.20 0.55 V/cm simple1 1.35 1.67 0.78 1.39 1.18 0.54simple2 1.36 1.54 0.72 1.42 1.26 0.58 ori/simple1 103% 105% 105% 103%102% 102% ori/simple2 102% 114% 114% 101%  95%  95%

This shows that use of the approaches described herein leads tosufficiently accurate electric field distributions in the head andcorrect field strength values, while being more time and computationallyefficient. Notably, the simplified model should be accurate enough foroptimization of electrode placement.

Additional details of the modeling of part 3 will now be discussed,including models in which simple convex hulls or shells are used tomodel the outer layers and a conductivity map is used to model thebrain. These models are able to account for anisotropic conductivity inthe cortical tissues by using tensor representation estimated fromDiffusion Tensor Imaging. The induced electric field distribution iscompared in the simplified and a realistic head model. The average fieldstrength values in the brain and tumor tissues are generally slightlyhigher in the realistic head model, with a maximal ratio of 114% for astandard simplified model (when reasonable thickness of layers areassured). It therefore provides a fast and efficient way towardspersonalized head models with a decreased degree of complexity betweentissue interfaces that enables accurate predictions about increasedelectric field distribution.

This study presents a first approach towards personalized head modelswhich would not need an underlying segmentation of the different headtissues. The method rather uses simple convex hulls to model the outerlayers and a conductivity representation of the cortical tissues derivedfrom a Diffusion Tensor Imaging (DTI) dataset.

A previously developed realistic human head model was used as a baselinemodel. An MRI dataset of a healthy, young, female was segmented intoscalp, skull, cerebrospinal fluid (CSF), gray matter (GM) including thecerebellum, white matter (WM), and ventricles. A virtual tumor locatedcentrally was modelled as two concentric spheres, an inner necrotic coresurrounded by an active tumor shell. The Optune™ system with a centralsymmetric layout was used for all calculations. FIG. 4, which is a frontview of the scalp 40 with the Optune™ transducer arrays 42, 44 affixedto the scalp depicts this layout. Note that only three of the fourpatches are visible in the figure and that neither the eyes nor the earsare represented on the convex hull. The final volume mesh was assembledwith Mimics aterialise.com).

Isotropic conductivity and permittivity values of the heterogeneoustissues were assumed as in previous studies and anisotropic conductivitytensors of the cortical tissues were estimated from Diffusion TensorImaging (DTI) data. Different approaches are assumed for the scaling ofthe diffusion tensors. In this example, only the direct mapping (dM)approach with the same scaling factor for each voxel was used. Furtherdetails are presented in The Electric Field Distribution in the BrainDuring TTFields Therapy and Its Dependence on Tissue DielectricProperties and Anatomy: A Computational Study by C, Wenger at al., Phys.Med. Biol., vol. 60, no, 18, pp. 7339-7357, 2015, which is incorporatedherein by reference.

One approach to simplify the model is to use convex hulls of the surfacemeshes instead of the complex and irregular geometry. In this study,convex hulls were created with MeshLab(http://meshlab.sourceforge.net/). The GM and the cerebellum wereapproximated as a single envelope, the WM, the scalp, the skull, and theCSF were represented by one convex hull each, FIGS. 5A and 5B depict thearrangement of the convex hulls (i.e., shells) for two similarsimplified models, called SHM1 (51) and SHM2 (52) respectively. In bothmodels, the convex hulls include the skull 54, the CSF 55 the greymatter (GM) 56, and the white matter (WM) 58. Note that the CSF 55 inSHM1 51 is very thin compared to the CSF 55 in SHM2 52. FIGS. 6A and 6Bdepict side and top views, respectively, of the ventricles 64 and thetumor 66 inside the WM convex hull 62. The ventricles and the tumortissues (active shell and necrotic core) remained unchanged.

Four different simple head models were developed (SHM1-SHM4). The first,SHM1, consists of the mentioned convex hulls which results in verydifferent tissue volumes compared to RHM. The WM is the innermost of thealtered tissues which is highly affected by applying a convex envelopewith a more than doubled tissue volume. This affects the surroundingtissues. The GM has a smaller volume in SHM1. The envelope over the GMgyri and the whole cerebellum reduces the volume of the CSF in SHM1. Theonly tissue with a slightly bigger volume in SHM1 compared to RHM is theskull which, in turn, results in a reduced volume of the scalp. Still,it shall be noted that the thickness of the scalp and skull layersunderneath the transducers are very similar in SHM1 and RHM, i.e., onaverage (of all 36 transducers) the ratio between layer thickness of RHMvs SHM1 is 102% in the scalp and 110% in the skull. Nonetheless, thisratio is 270% for the CSF. Thickness was estimated with the volume ofintersecting cylinders, i.e., a cylinder was created extending thetransducer and then the intersecting volume with the next tissue surfacewas calculated. Thus, the higher volume of the CSF cylinders of RHM isattributed to the additional volume resulting from the sulci instead ofa plane GM as in SHM1.

A second simple model SHM2, was created to reduce these discrepancies,i.e., the altered tissue volumes and the minimal CSF thickness in SHM1(as seen in FIG. 5A). SHM2 resulted from scaling meshes in Mimics: theWM and GM simultaneously by a factor of 0.97 followed by scaling the CSFwith a factor of 0.995. This resulted in decreased differences of layerthickness for SHM2 compared to RHM of 102% for the scalp, 100% for theskull and 128% for the CSF. These two models were first solved asisotropic and anisotropic models and compared to the RHM results. Theestimation of the conductivity tensors with DTI data remained unchanged.Note that in RHM all DTI data outside the GM boundary was disregarded.The diffusion information for all additional voxels that are part of theGM convex hull in SHM1 and SHM2 were added.

SHM3 is a simpler model that only uses one convex hull for the corticaltissues, leaving out the boundary between WM and GM. As a lastsimplification step, SHM4 further cuts the ventricles and only workswith the conductivity data derived from DTI, instead of an isotropicCSF-filled chamber in all other models.

In order to calculate the electric field distribution, the finiteelement (FE) software Comsol Multiphysics (http://www.comsol.com) wasused to solve the quasi-static approximation of the Maxwell equations inthe frequency domain with 200 kHz, Isotropic and anisotropic materialproperties were already discussed. Boundary conditions assumedcontinuity of the normal component at inner boundaries, electricinsulation at outer boundaries. TTFields activation was simulated withFloating Potential conditions with 100 mA for each active transducer.

The results of the study are as follows. Each model setup (type ofmodel, isotropic or dM representation of the brain conductivities) issolved for both array field directions, LR and AP.

The first simulations were carried out with the SHM1 model and theisotropic and anisotropic solutions were compared to those of the RHMmodel. This initial simplified model, SHM1 with its thin CSF produceshigh electric field strength values in the brain and tumor tissues(Table 2). When adapting the CSF thickness introduced by SHM2, theobtained average field strength values are very similar and slightlydecreased in the tumor compared to RHM. As presented in Table 2 thehighest increase is 107% reported for the average field strength in thetumor shell under LR activation and isotropic conductivities.

FIG. 7 contains five panels 71-75, each cif depicts the conductivity mapand resulting electric field distributions in the cortical and tumortissues in an axial slice for a respective model. In each panel 71-75,the trace of the conductivity tensor appears on top, where the legendfor the tensor trace is fixed and ranges from 0.1-0.6 S/m. The color ofthe tumor tissues is arbitrary in this figure. In each panel theelectric field distribution for the LR and AP electrodes appears in themiddle and bottom, respectively, and the intensity legend ranges from0-4 V/cm.

Panels 71 and 72 illustrate the isotropic RHM and SHM2 model with theirisotropic brain and tumor conductivities. Although the electric fielddistribution in the brain has only minor detail in SHM2 the fielddistribution in the tumor is similar for both LR and AP setups and theinduced average field strength are similar (Table 2). When anisotropy isintroduced for the brain tissues the field distribution in the brain ofthe RHM model is only slightly altered (compare panels 71 and 73); andthe SHM2 anisotropic model (panel 74) shows increased detail and thecalculated average field strength values are more coherent with those ofthe anisotropic RHM model (panel 73).

The SHM2 model (panel 74) was taken as baseline model for the furthersimplifications of SHM3 and SHM4 described above. Given the fact thatthe GM and WM are only represented by two convex hulls, no effect wasexpected from removing the inner shell, since the dM approach was usedfor scaling of the conductivity tensors. Indeed, almost no changes werefound in the average field strength values (Table 2).

The ventricles are a complex structure in the center of the brain filledwith CSF and thus are considered to be isotropic. Thus, the informationestimated from DTI data is usually omitted for electric fieldcalculations with realistic head models and a detailed segmentation withisotropic conductivities is used. SHM4 was created to investigate theeffect of neglecting the segmentation of the ventricles and accountingfor their presence by using the tensor evaluated from the DTI dataset.The resulting trace of the conductivity tensor is displayed in the topof panel 75. The average field strength in the brain is only slightlyhigher in RHM than in SHM4 (102% in LR and 101% in AP). In the tumorshell the highest field strength increase in RHM compared to the SHM4model is 114% for LR (Table 2). This provides an indication that despitethe additional simplification introduced in the SHM4 model, the resultsare still acceptable.

Table 2 depicts variations in field strength between the various modelsin both the LR and AP directions. Note that SHM3 and SHM4 in Table 2correspond, respectively, to the Simple1 and Simple2 models in table 1above.

TABLE 2 Average Field Strength (V/cm) in the Brain and Tumor Tissues inDifferent Models LR AP Model conductivity brain shell brain Shell RHMiso 1.41 1.59 1.43 1.13 SHM1 iso 1.93 1.88 1.98 1.37 SHM2 iso 1.53 1.491.56 1.10 RHM/SHM1  73%  85%  72%  82% RHM/SHM2  92% 107%  92% 103% RHManiso dM 1.39 1.76 1.43 1.20 SHM1 aniso dM 1.64 2.06 1.69 1.41 SHM2aniso dM 1.35 1.67 1.38 1.17 SHM3 aniso dM 1.35 1.67 1.39 1.18 SHM4aniso dM 1.36 1.54 1.42 1.26 RHM/SHM1  85%  85%  84%  85% RHM/SHM2 103%105% 103% 102% RHM/SHM3 103% 105% 103% 102% RHM/SHM4 102% 114% 101%  95%

The presented approach can be used to rapidly create head models ofpatients with GBM for personalized treatment plans of TTFields. Thescalp outline could be obtained by segmenting a structural image withknown software in a minimum amount of time. Alternatively, headmeasurements could be used to predict the overall head shape. Followinglayers (skull, CSF, brain) could be created by thickness measurementsfrom the structural image. Summarizing, the proposed technique should beeasily applicable for future modeling, since the convex hulls outsidethe brain can be generated generically with the measurements of the headas only input. As for the tumor and the brain itself, a DTI dataset forthe patient is used to determine the dielectric properties (e.g.,conductivity).

The acquisition of DTI is not standard, however, Diffusion Weightedimaging (DWI) with less direction is quite commonly acquired and thetrace of the conductivity tensor can be estimated by only threedirections. In alternative embodiments, the induced field distributioncan be determined using only the trace values in each voxel and not thefull tensor. This would provide an additional simplification of themodel, at the possible expense of accuracy.

DTI is still a relatively new technique and image resolution is quitelow (i.e., >1 mm³ isotropic). As a result, careful choice of imagecorrection and tensor estimation method is important and appropriateinterpolation method is advisable. For scaling the diffusion tensor tothe conductivity tensor two methods are introduced. Additionally to thedM approach, in the volume normalized (vN) method the geometric mean ofthe eigenvalues are matched to the isotropic reference values for eachvoxel. To accomplish that an underlying segmentation of the tissue typemay be implemented. In some embodiments, the estimated trace of thetensor in each voxel could be used to classify the tissue type and serveas a proxy for segmentation.

As already pointed out, there already exist automated segmentationalgorithms for detailed GBM segmentation. An example of a publiclyavailable algorithm is the recent Brain Tumor Image Analysis (BraTumIA)software which distinguishes necrotic core, edema, non-enhancing tumorand enhancing tumor while needing four different imaging modalities (T1,T1-contrast, T2-contrast, and FLAIR). Techniques which only need a T1 asinput also exist. Still, the heterogeneous environment of a GBM andsurrounding edema might even be depicted in more detail with avoxel-wise tensor representation. Thus, although the simplified modelhas reduced complexity, it can still be used to describe the electricfield distribution of TTFields in more detail.

This section (i.e., part 3) presents a first attempt to create simplehead models which provide accurate results for calculating the electricfield distribution for the application of TTFields. The electric fieldstrength in one central tumor did not change significantly when using asimple model compared to a realistic human head model derived fromstructural images. The method described herein can be extended to createpersonalized models without the need for time-consuming tissuesegmentation. In future, this method could be used to rapidly developindividual patient head models with a detailed representationof theirlesion, albeit with the requirement that a DTI dataset is available.

Once the layout that optimizes the electric field within the diseasedregions of the patient's brain has been determined (e.g., using any ofthe approaches explained herein), the electrodes are positioned in thedetermined positions. AC voltages are then applied to the electrodes(e.g., as described in U.S. Pat. No. 7,565,205, which is incorporatedherein by reference) to treat the disease.

Note that the concepts described herein are not limited to using DTI toderive the electric properties of the brain. To the contrary—it extendsto other methods that can be used for the same purpose including but notlimited to DWI, Electric Conductivity imaging, Electric ImpedanceTomography (EIT) and multi echo GRE.

Note also that the concepts described herein are not limited torepresentations of the outer layers (scalp, skull, CSF) as convex hulls,and other methods may be used to roughly approximate the MRI data.Examples include simple geometric forms such as ellipsoids, spheres,oval shaped structure or also other methods for creating an envelope ofthe tissues. Additionally, the concepts described herein are notrestricted to an approximation of the outer layers, i.e., the scalp,skull and CSF layers can also be obtained through conventionalsegmentation of MRIs.

Optionally, post-processing of conductivity maps to improve results (e.gsmoothing or outlier removal/replacement, adapted interpolationtechniques, etc.) may be implemented. Furthermore, other mapping methodsfrom diffusion to conductivity methods may be used, as well as acombination of the two mentioned methods (e.g., the dM and vN approach).Thus, it may be advantageous to use the dM for the cortical tissues, andthe vN for the ventricles and the tumor tissues including an edemaregion which all might have been identified as regions of interest(ROIs) by a clinician or radiologist.

Some of the embodiments described above use a mixed method in which somevolume elements are assigned representative electric properties of thetissue types they belong to, whereas others are assigned electricproperties based on the specific MRI sequence data (in this case DTI).For example, the skull, scalp and CSF were assigned representativeisotropic dielectric properties, whereas the conductivities of the whiteand grey matter (and ventricles in some embodiments) were derived fromthe DTI data. Note that in the presented case also the tumor tissueswere assigned isotropic dielectric properties at a virtual location,since the images originated from a healthy subject. In alternativeembodiments, however, total amount of volume elements within the wholehead may be assigned either isotropic or anisotropic dielectricproperties that were solely derived from a specific imaging technique.

Note that in some embodiments, only the boundary surface of the head isidentified, e.g., by conventional segmentation of the scalp surface, andconductivity and/or permittivity are assigned to all points within thephantom using the conductivity measurements derived from the MRIconductivity measurements.

In some embodiments, the brain is identified using existing whole brainextraction algorithms. Next, the scalp, skull, and CSF are segmentedusing an automatic procedure. Conductivity values are assigned to thebrain, the tumor tissues (including active shell and necrotic core), apossible edematous region, and the ventricles using the MRI conductivitymeasurements. Bulk conductivity values are assigned to the scalp, skull,and CSF.

In some embodiments, the brain is identified using existing whole brainextraction algorithms. Next, the scalp, skull, CSF, and ventricles aresegmented using an automatic procedure. Conductivity values are assignedto the brain, the tumor tissues (including active shell and necroticcore), and a possible edematous region using the MRI conductivitymeasurements. Bulk conductivity values are assigned to the scalp, skull,CSF, and ventricles.

In some embodiments, the brain is identified using existing whole brainextraction algorithms. The tumor is marked as a ROI by a clinician orradiologist. Next, the scalp, skull and CSF are segmented using anautomatic procedure. Conductivity values are assigned to the brain andthe ventricles using the MRI conductivity measurements. Bulkconductivity values are assigned to the scalp, skull, CSF, and the tumortissues (e.g., by assigning a constant conductivity value to each ofthose regions).

Note also that instead of using the segmentation of the scalp, skull,and CSF, an approximation of these outer layers may be used. Forexample, the user may be asked to measure the thickness of the scalp,skull, and CSF in a representative region. These tissues are thenapproximated as concentric geometric entities similar to a defaultconvex hull of a scalp, a sphere, an ellipsoid, etc.) with theuser-measured thicknesses surrounding the brain. This approximationsimulates the head as an (almost) oval shaped structure, ignoringfeatures such as the ears, nose, mouth and jaw. However, since thearrays and treatment are delivered only to the supratentorial region ofthe head, this approximation appears to be justified. In someembodiments it might also be possible to combine two or more of thethree tissue types into one layer and assign a single conductivity valueto that layer. For instance, the scalp and skull may be introduced asone layer with a single conductivity (and optionally a uniformthickness).

The inventors expect that the ability to develop realistic head modelsfor individual patients will not only allow for optimization of theelectric field within the tumor, but may also enable treatment planningthat mitigates out-of-field reoccurrences. This could be achieved bydeveloping optimization methods that not only account for the electricfield intensity within the tumor, but also try to optimize the fieldintensity in other regions of the brain.

Optionally, patient-specific computational head models may be used forretrospective patient analysis that could clarify the connection betweenfield strength distributions and disease progression within patients,ultimately leading to a better understanding on how to deliver TTFieldsin patients.

Computational phantoms built in this manner could also be used for otherapplications in which calculating electric field and or electric currentdistributions within the head may be useful. These applications include,but are not limited to: direct and alternating current trans-cranialstimulation; simulations of implanted stimulatory electrode field maps;planning placement of implanted stimulatory electrodes; and sourcelocalizationin EEG.

Finally, although this application describes a method for optimizingarray layouts on the head, it could potentially be extended foroptimizing array layouts for treatment of other body regions such as thethorax or abdomen.

While the present invention has been disclosed with reference to certainembodiments, numerous modifications, alterations, and changes to thedescribed embodiments are possible without departing from the sphere andscope of the present invention, as defined in the appended claims.Accordingly, it is intended that the present invention not be limited tothe described embodiments, but that it has the full scope defined by thelanguage of the following claims, and equivalents thereof.

What is claimed:
 1. A method of creating a model of a mammal's head, the head including brain tissue, CSF, a skull, and a scalp, the method comprising the steps of: modeling a region of the head that corresponds to brain tissue using a 3D set of conductivity tensors; and modeling the CSF, the skull, and the scalp using at least one shell having a constant conductivity.
 2. The method of claim 1, wherein the step of modeling the region of the head that corresponds to brain tissue using a 3D set of conductivity tensors is implemented without identifying boundaries between different types of a healthy brain tissue.
 3. The method of claim 1, wherein the 3D set of conductivity tensors is obtained using MRI.
 4. The method of claim 3, wherein the 3D set of conductivity tensors is derived from a diffusion tensor imaging dataset.
 5. The method of claim 1, wherein the step of modeling the CSF, the skull, and the scalp comprises the steps of: modeling the CSF as a first shell disposed outside the brain tissue and in contact with the brain tissue, the first shell having a first constant conductivity; modeling the skull as a second shell disposed outside the CSF and in contact with the CSF, the second shell having a second constant conductivity; and modeling the scalp as a third shell disposed outside the skull and in contact with the skull, the third shell having a third constant conductivity.
 6. The method of claim 1, wherein the step of modeling the CSF, the skull, and the scalp comprises the step of: modeling the CSF, the skull, and the scalp, taken together, as a single shell disposed outside the brain tissue and in contact with the brain tissue, the single shell having a constant conductivity.
 7. The method of claim 1, further comprising the steps of: identifying a location of a target tissue within the brain tissue; and determining positions for a plurality of electrodes on the mammal's head based on the location of the target tissue identified in the identifying step, the 3D set of conductivity tensors, and the conductivity of the at least one shell.
 8. The method of claim 7, further comprising the steps of: affixing the electrodes to the mammal's head at the positions determined in the determining step; and applying electrical signals between the electrodes subsequent to the affixing step, so as to impose an electric field in the target tissue.
 9. The method of claim 7, wherein the step of determining positions for the electrodes comprises modeling a dipole at a location that corresponds to the target tissue and selecting positions at which a potential attributable to the dipole is maximum.
 10. The method of claim 7, wherein the step of determining positions for the electrodes comprises calculating positions for the electrodes that will provide optimal combined treatment specifications in the target tissue.
 11. The method of claim 1, wherein the step of modeling a region using a 3D set of conductivity tensors comprises classifying a tissue type for each volume element based on a fractional anisotropy.
 12. The method of claim 1, wherein the step of modeling a region using a 3D set of conductivity tensors comprises classifying a tissue type for each volume element based on a mean conductivity.
 13. The method of claim 1, wherein the step of modeling a region using a 3D set of conductivity tensors comprises matching geometric means of conductivity tensors' eigenvalues to specific isotropic reference values.
 14. The method of claim 1, wherein a composite model is generated in which the modeled region of the head that corresponds to brain tissue is surrounded by the modeled CSF, skull, and scalp using the at least one shell. 